What is the Normal Force Acting on a Chair with a Box on a Slanted Slope?

[BSCS]

I'm trying to think up situations that will help me understand more complicated situations...

Let's say I have:

a box
on a slanted slope
on a chair
on the floor

The floor exerts a normal force on the chair. But, equal to what?

is it:

a box $$m_{1}gcos\theta$$

on a slanted slope $$m_{2}g$$

on a chair $$m_{3}g$$

on the floor

Is it the sum of these?

Also, would motion of the box along the inclined plane affect the result? It would seem to be "no".

 

[Hootenanny]

Have you tried drawing a FBD?

 

[BSCS]

Yes, and it/they were getting complex, so I wanted to get some feedback. I came up with the force exerted down on the chair as having an x component and a y component (different from what I posted). From there I was thinking I could apply that vector to the FBD of the chair and come up with my answer. Is such a "cascading of forces" approach correct?

 

[Hootenanny]

Yes, and it/they were getting complex, so I wanted to get some feedback. I came up with the force exerted down on the chair as having an x component and a y component (different from what I posted). From there I was thinking I could apply that vector to the FBD of the chair and come up with my answer. Is such a "cascading of forces" approach correct?

Yes, from what I understand you to have described that is correct. Perhaps if you posted you FBD's we could comment further.

 

[Doc Al]

Let's say I have:

a box
on a slanted slope
on a chair
on the floor

The floor exerts a normal force on the chair. But, equal to what?

is it:

a box $$m_{1}gcos\theta$$

on a slanted slope $$m_{2}g$$

on a chair $$m_{3}g$$

on the floor

Is it the sum of these?

Huh? Are you describing one situation (a box on a chair which is on a slanted slope?) or multiple situations? What are those masses?